Bending pieces of an object
for this part of your object, you'd rather:


Begin with a cubic shape.
Add some vertical edge loops.
Round the faces with the Proportional Editing option (Sphere Falloff mode).
Give it a Solidify modifier.
Round the angle edges with bevels (ctrl B).
Smooth your object with a Subdivision Surface modifier.
Sharpen the edges with additional edge loops.
When you're happy with the thickness, apply the Solidify.